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A 93 kg astronaut and a 1400 kg satellite are at rest relative tothe space shuttle. The astronaut pushes on the satellite, giving ita speed of 0.15 m/s directly away from the shuttle. Seven and ahalf seconds later the astronaut comes into contact with theshuttle.

What was the initial distance from the shuttle to theastronaut?

Answer :

boffeemadrid

Answer:

16.93545 m

Explanation:

[tex]m_1[/tex] = Mass of astronaut = 93 kg

[tex]m_2[/tex] = Mass of satellite = 1400 kg

[tex]v_1[/tex] = Velocity of astrounaut

[tex]v_2[/tex] = Velocity of satellite = 0.15 m/s

As linear momentum of the system is conserved

[tex]m_1v_1+m_2v_2=0\\\Rightarrow v_1=-\frac{m_2v_2}{m_1}\\\Rightarrow v_1=-\frac{1400\times 0.15}{93}\\\Rightarrow v_1=2.25806\ m/s[/tex]

As there is no acceleration

Distance = Speed × Time

[tex]Distance=2.25806\times 7.5=16.93545\ m[/tex]

The initial distance from the shuttle to the astronaut is 16.93545 m

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